Question: Rewrite as a simplified fraction. ${1.6\overline{75} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1675.7575...\\ 10x &= 16.7575...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1659}$ ${x = \dfrac{1659}{990}} $ ${x = \dfrac{553}{330}} \text{or} {1 \dfrac{223}{330}}$